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Quantitative Biology > Other Quantitative Biology

Abstract: The article is devoted to phenomena of symmetries and algebras in matrix
presentations of the genetic code. The Kronecker family of the genetic matrices
is investigated, which is based on the alphabetical matrix [C A; U G], where C,
A, U, G are the letters of the genetic alphabet. The matrix P=[C A; U G] in the
third Kronecker power is the (8*8)-matrix, which contains 64 triplets.
Peculiarities of the degeneracy of the genetic code are reflected in the
symmetrical black-and-white mosaic of this genetic (8*8)-matrix of 64 triplets.
Phenomena of connections of this mosaic matrix (and many other genetic
matrices) with projection operators are revealed. Taking into account an
important role of projection operators in quantum mechanics, theory of digital
codes, computer science, logic and in many other fields of applied mathematics,
we study algebraic properties and biological meanings of these phenomena. Using
of notions and formalisms of theory of finite-dimensional vector spaces in
bioinformatics and theoretical biology is proposed on the bases of the
described results.